Are they connected through a wireless network? I had problems with my wireless network that it would disconnect me when someone answered the phone and sometimes it just happened around 6 p.m. I was rarely disconnected at night also.
since u are using cable the internet speed depends on what the other people using the same cable connection are doing. (usually this means people living close to u with the same ISP provider) So during the day if a lot of people are downloading stuff etc the connection can get quite slow, meaning ur ping is high and u get kicked from the server. It doesn't happen during the night so much because at night there are not so many people using their cable connection.
Thats just one possibility, but thats all that I can think of right now.